Approximating identity-by-descent matrices using multiple haplotype configurations on pedigrees

Abstract

Identity-by-descent (IBD) matrix calculation is an important step in quantitative trait loci (QTL) analysis using variance component models. To calculate IBD matrices efficiently for large pedigrees with large numbers of loci, an approximation method based on the reconstruction of haplotype configurations for the pedigrees is proposed. The method uses a subset of haplotype configurations with high likelihoods identified by a haplotyping method. The new method is compared with a Markov chain Monte Carlo (MCMC) method (Loki) in terms of QTL mapping performance on simulated pedigrees. Both methods yield almost identical results for the estimation of QTL positions and variance parameters, while the new method is much more computationally efficient than the MCMC approach for large pedigrees and large numbers of loci. The proposed method is also compared with an exact method (Merlin) in small simulated pedigrees, where both methods produce nearly identical estimates of position-specific kinship coefficients. The new method can be used for fine mapping with joint linkage disequilibrium and linkage analysis, which improves the power and accuracy of QTL mapping.

Figure 1.

Average test statistic (log LR) profiles over 50 replicated pedigrees of size 470–500, with 10 biallelic markers, intermarker distance of 5 cM, true QTL position at 22.5 cM, and QTL variance at 10% of the trait variance. IBD matrices were calculated in three ways: “New1” and “New2,” which denote the proposed method with λ = 0.65, α = −0.3, and n_s = 50 and with λ = 0.90, α = −1.0, and n_s = 50, respectively, and “Loki,” which represents use of the Loki software with 100,000 iterations. See main text for explanation of control parameters λ, α, and n_s.

Figure 2.

Test statistic (log LR) profile for a pedigree of 1024 individuals, with 50 biallelic markers, intermarker distance of 1 cM, true QTL position at 24.5 cM, and QTL variance at 18% of the trait variance. IBD matrices were calculated with the proposed method using control parameter values of λ = 0.65, α = −0.3, and n_s = 50.

Figure 3.

Test statistic (log LR) profiles obtained using the new IBD matrix calculation method with different values of control parameters λ, α, and n_s for a single pedigree. The pedigree had 483 individuals with 10 biallelic markers, true QTL position at 22.5 cM, and intermarker distance of 5 cM. A denotes the profile of log LR with λ = 0.65, α = −0.3, and n_s = 50; B, the profile with λ = 0.65, α = −0.3, and n_s = 1000; C, the profile with λ = 0.90, α = −1.0, and n_s = 50; and D, the profile with λ = 0.90, α = −1.0, and n_s = 1000.

Figure 4.

Average test statistic (log LR) profiles over 50 replicated pedigrees of size 480–510, with 20 biallelic markers, intermarker distance of 1 cM, true (biallelic) QTL position at 9.5 cM, and QTL variance at 10% of the trait variance. IBD matrices were calculated with the proposed method incorporating linkage disequilibrium. New1 denotes the new IBD matrix method with λ = 0.65, α = −0.3, and n_s = 50; New2 has λ = 0.90, α = −1.0, and n_s = 50; and New3 has λ = 0.90, α = −1.0, and n_s = 1000.